Dynamic response of a monorail steel bridge under a moving train

This study proposes a dynamic response analysis procedure for traffic-induced vibration of a monorail bridge and train. Each car in the monorail train is idealized as a dynamic system of 15-degrees-of-freedom. The governing equations of motion for a three-dimensional monorail bridge-train interaction system are derived using Lagrange's formulation for monorail trains, and a finite-element method for modal analysis of monorail bridges. Analytical results on dynamic response of the monorail train and bridge are compared with field-test data in order to verify the validity of the proposed analysis procedure, and a positive correlation is found. An interesting feature of the monorail bridge response is that sway motion is caused by torsional behavior resulting from eccentricity between the shear center of the bridge section and the train load.     

Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system’s vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.     

Stability analysis of hydro-turbine governing system based on machine learning

Hydro-turbine governing system is a time-varying complex system with strong non-linearity, and its dynamic characteristics are jointly affected by hydraulic, mechanical, electrical, and other factors. Aiming at the stability of the hydro-turbine governing system, this paper first builds a dynamic model of the hydro-turbine governing system through mechanism modeling, and introduces the transfer coefficient characteristics under different load conditions to obtain the stability category of the system. BP neural network is used to perform the machine study and the predictive analysis of the stability of the system under different working conditions is carried out by using the additional momentum method to optimize the algorithm. The test set results show that the method can accurately distinguish the stability category of the hydro-turbine governing system (HTGS), and the research results can provide a theoretical reference for the operation and management of smart hydropower stations in the future.     

Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles

An investigation into the dynamics of vehicle-occupant-structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of the dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span, while the maximum bending moment occurs at ±20% of the mid-span point. It is shown that one can find a critical speed at which the maximum values of the bridge dynamic deflection and the bending moment attain their global maxima.     

An elastic-perfectly plastic model for simulating an aluminum particle behavior during plasma thermal spraying using the finite element method

It is a 2D numerical study which treats the splat and flattening of the droplet during a thermal spraying process. An aluminum particle at a high temperature is impacted on steel substrate. A perfectly elastic-plastic model is used instead of the VOF method which is exclusively used in the literature. For this purpose, the finite element method with Ansys mechanical APDL program is used to solve the governing equations. Displacement, elastic and plastic strains, Von-Mises stress, energy densities, and contact pressure are evaluated during the impact of the particle. Additionally, it is found that the initial impact velocity has a significant effect on splat behavior. This mechanical model gives a promise results that can be improved to help understand the impact and flattening phenomenon.     

Studies of material constitutive behavior using perturbation growth in explosive and magnetically driven liner systems

This paper discusses a collaborative research program aimed at the development of improved constitutive modeling capability, in particular, the development of a model validated over a wide range of strain rates (from quasistatic to 10⁶ s⁻¹). This program includes experimental, theoretical, and numerical components. The experimental part of the program includes both planar and cylindrical manifestations of the perturbation growth method. The theoretical part of the program is focused on the development of a model that considers all the necessary physical aspects and, at the same time, is compatible with standard numerical methods for solving the governing field equations. The numerical part of the program is focused on model implementation (in an appropriate continuum mechanics code) and validation. All three parts of the program are coupled. This paper will discuss the experimental program, the development of a new model, and show some results comparing various model predictions to experimental data. The text was submitted by the authors in English.     

非定常粘性空化流动模型及其数值计算

基于气液两相当地均相介质模型,本文给出了一种模拟非定常粘性空化流动的计算模型。认为空化绕流流场中流动介质是一种当地均匀的气液混相物。控制方程采用了应用两相流模型的N-S方程。基于液相和气相的状态方程推导了混合介质密度的表达式。为了保证数值计算的稳定性,控制方程的数值求解采用了TVD-MacCormack格式。为了评价计算模型的可靠性,分别计算了绕台阶和管道水锤的空化流动,所得结果是合理的,说明该方法可以用于空化流动的数值计算。     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

VIBRATION ANALYSIS OF A DAMPED ARCH USING AN ITERATIVE LAMINATE MODEL

A new model is presented for the dynamic analysis of a laminated circular ring segment. The differential equations which govern the free vibrations of a circular ring segment and the associated boundary conditions are derived by Hamilton's principle having consideration for the bending and shear deformation of all layers. The author uses a new iterative process to successively refine the stress/strain field in the sandwich arch. The model includes the effects of transverse shear and rotatory inertia. The iterative model is used to predict the modal frequencies and damping of simply-supported sandwich circular arch. The solutions for a three-layer circular arch are compared with a three-layer approximate model.     

活性布朗粒子运动的稳态解

拟可积Hamilton系统随机平均法可以用来研究活性布朗粒子运动.介绍了该随机平均法，利用它详细求解了布朗粒子运动的动力学方程，该方程描述了活性布朗粒子在平面上的运动，粒子受到的激励是Gaussian白噪声，受到的阻尼是Schienbein-Gruler速度依赖的磨擦模型.通过与数字模拟和与实验数据的比较，证明所得稳态解正确.对于Rayleigh和Erdamnn速度依赖的磨擦模型，也给出了稳态解. 关键词： 活性布朗粒子 拟可积Hamilton系统随机平均法 可积性 稳态解     

Dynamic analysis of double-row self-aligning ball bearings due to applied loads,internal clearance,surface waviness and number of balls

In this paper, a three degrees of freedom (dof) model was established for a double-row self-aligning ball bearing (SABB) system, and was applied to study the dynamic behavior of the system during starting process and constant speed rotating process. A mathematical model was developed concerning stiffness and damping characteristics of the bearing, as well as three-dimensional applied load, rotor centrifugal force, etc. Balls and races were all considered as nonlinear springs, and the contact force between ball and race was calculated based on classic Hertzian elastic contact deformation theory and deformation compatibility theory. The changes of each ball?s contact force and loaded angle of each row were taken into account. In order to solve the nonlinear dynamical equilibrium equations of the system, these equations were rewritten as differential equations and the fourth order Runge–Kutta method was used to solve the equations iteratively. In order to verify accuracy of the dynamical model and correctness of the numerical solution method, a kind of SABB-BRF30 was chosen for case studies. The effects of several important governing parameters, such as radial and axial applied loads, normal internal, inner and outer races waviness, and number of balls were investigated. These parametric studies led to a complete characterization of the shaft-bearing system vibration transmission. The research provided a theoretical reference for new type bearing design, shaft-bearing system kinetic analysis, optimal design, etc.     

Dynamic characteristics of traveling waves for a rotating laminated circular plate with viscoelastic core layer

The dynamic governing equations and the corresponding boundary conditions for a rotating thin laminated circular plate with a viscoelastic core layer are derived in this paper based on the Hamilton principle. The analysis on dynamic features of the forward and Backward Traveling Waves for the rotating laminated plate is performed by means of Galerkin's method. The frequency-dependent complex modulus model for describing the constitutive behavior of the viscoelastic core layer is employed. The dynamic characteristics of frequencies and dampings of traveling waves for the rotating plate are obtained numerically. The effects of geometrical and material parameters on the critical speed of the rotating laminated plate with viscoelastic core are discussed in detail.     

Numerical Simulations of Unsteady Flows from Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm

Numerical simulations of unsteady gas flows are studied on the basis of Gas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flow regimes. Several typical examples are adopted. An unsteady flow solver is developed by solving the Boltzmann model equations, including the Shakhov model and the Rykov model etc. The Rykov kinetic equation involving the effect of rotational energy can be transformed into two kinetic governing equations with inelastic and elastic collisions by integrating the molecular velocity distribution function with the weight factor on the energy of rotational motion. Then, the reduced velocity distribution functions are devised to further simplify the governing equation for one- and two-dimensional flows. The simultaneous equations are numerically solved by the discrete velocity ordinate (DVO) method in velocity space and the finite-difference schemes in physical space. The time-explicit operator-splitting scheme is constructed, and numerical stability conditions to ascertain the time step are discussed. As the application of the newly developed GKUA, several unsteady varying processes of one- and two-dimensional flows with different Knudsen number are simulated, and the unsteady transport phenomena and rarefied effects are revealed and analyzed. It is validated that the GKUA solver is competent for simulations of unsteady gas dynamics covering various flow regimes.     

Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation

Instantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. The procedure of decomposition is valid for weakly nonlinear flows, resulting in the nonlinear terms responsible for the modes interaction. Nonlinear acoustic terms form a source of acoustic heating in the case of dominative sound, which reflects the thermoviscous and dispersive properties of a fluid. The method of deriving the governing equations does not need averaging over the sound period, and the final governing dynamic equation of the thermal mode is instantaneous. Some examples of acoustic heating are illustrated and discussed, conclusions about efficiency of heating caused by different sound impulses are made.     

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.     

Mesoscopic approach to inviscid gas dynamics with thermal lag

A phenomenological model for thermal relaxation and wave propagation in ideal polyatomic gases is developed by introducing a dynamical non‐equilibrium temperature. The system of equations governing the evolution of the gas is derived and the speeds of propagation of thermo‐mechanical disturbances together with the Rankine‐Hugoniot jump conditions for shock waves are calculated. The hyperbolic theories of heat propagation in incompressible fluids and rigid solids are recovered as particular cases. For rigid solids, the well posedness of the Cauchy problem is proved by a classical method.     

变系数瞬态热传导问题边界元格式的特征正交分解降阶方法

提出了一种基于边界元法求解变系数瞬态热传导问题的特征正交分解(POD)降阶方法,重组并推导出变系数瞬态热传导问题适合降阶的边界元离散积分方程,建立了变系数瞬态热传导问题边界元格式的POD降阶模型,并用常数边界条件下建立的瞬态热传导问题的POD降阶模态,对光滑时变边界条件瞬态热传导问题进行降阶分析.首先,对一个变系数瞬态热传导问题,建立其边界域积分方程,并将域积分转换成边界积分;其次,离散并重组积分方程,获得可用于降阶分析的矩阵形式的时间微分方程组;最后,用POD模态矩阵对该时间微分方程组进行降阶处理,建立降阶模型并对其求解.数值算例验证了本文方法的正确性和有效性.研究表明:1)常数边界条件下建立的低阶POD模态矩阵,能够用来准确预测复杂光滑时变边界条件下的温度场结果;2)低阶模型的建立,解决了边界元法中采用时间差分推进技术求解大型时间微分方程组时求解速度慢、算法稳定性差的问题.     

A parametric multi-body section model for modal interactions of cable-supported bridges

A parametric section model is formulated to synthetically describe the geometrically nonlinear dynamics of cable-stayed and suspended bridges through a planar elastic multi-body system. The four-degrees-of-freedom model accounts for both the flexo-torsional motion of the bridge deck and for the transversal motion of a pair of hangers or stay cables. After linearization around the pre-stressed static equilibrium configuration, the coupled equations of motion governing the global deck dynamics and the local cable motion are obtained. A multi-parameter perturbation method is employed to solve the modal problem of internally resonant systems. The perturbation-based modal solution furnishes, first, explicit formulae for the parameter combinations which realize the internal resonance conditions and, second, asymptotic approximations of the resonant frequencies and modes. Attention is focused on the triple internal resonance among a global torsional mode of the deck and two local modes of the cables, due to the relevant geometric coupling which maximizes the modal interaction. The asymptotic approximation of the modal solution is found to finely describe the multiple veering phenomenon which involves the three frequency loci under small variation of the most significant mechanical parameters, including terms of structural coupling or disorder. Moreover, the veering amplitude between any two of the three frequency loci can be expressed as an explicit parametric function. Finally, the disorder is recognized as the only parameter governing a complex phenomenon of triple modal hybridization involving all the resonant modes. The entire hybridization process is successfully described by an energy-based localization factor, presented in a new perturbation-based form, valid for internally resonant system.